While electrical transport has been the focus of intensive research for over half a century, thermal transport has been much more challenging to quantify and model. However, as devices continue to shrink, effective heat transfer will soon loom as the Achilles’ heel to Moore’s law. While modeling nanoscale electronic transport, I often thought about possible parallels with phonons and became interested in providing a similar ab-initio footing for thermal transport. Developing a first principles technique to model thermal conductivity is difficult because both harmonic and anharmonic phonon interactions must be taken into account. The force constants associated with these interactions can be calculated in the framework of density functional perturbation theory, but existing codes can only calculate anharmonic terms at special points in the Brillouin zone. However in order to determine the thermal conductivity of a material, you must calculate anharmonic interactions between numerous k-points in the Brillouin zone. This requirement dictates expanding existing codes or else developing a new approach.

To address thermal transport in nanoscale systems, I have combined my knowledge of first principles techniques with experts on the self-consistent Boltzmann-Peierls approach (Prof. David Broido, Boston College) and phonon transport using non-equilibrium Green’s functions (Dr. Natalio Mingo, CEA Grenoble). Using harmonic and anharmonic interactions derived from first principle calculations, we can provide estimates for bulk system thermal conductivity (linking with the Boltzmann-Peierls approach) and nanoscale structures (linking with NEGF models of phonon transport). Our approach provides a better estimate of bulk silicon and germanium thermal conductivity than alternative models based on empirical potentials1 . In recent years, we have expanded this effort to consider other materials. We have been able to accurately predict the thermal conductivity of diamond2 and thermoelectric materials like Mg2SixSn1-x alloys and SiGe alloys with embedded nanoparticles. This research program has been supported by two grants from NSF.

Unlike many of their bulk counterparts, impurities, defects, and even isotopes can have a significant effect on the properties of nanostructures like carbon nanotubes and silicon nanowires. Working with Natalio Mingo and Ivana Savic (CEA-Grenoble), I am examining the role of imperfections on nanoscale thermal conductance. We recently investigated how different defects would affect phonon transmission in carbon nanotubes, looking in particular at a Stone-Wales defect and a nitrogen impurity. In the case of nitrogen substitution, only high frequency phonon transmission is affected where the phonon wavelength is comparable to the length scale of the nitrogen impurity. In contrast, the Stone-Wales defect reconfigures local carbon bonds and breaks the original nanotube symmetry, reducing the phonon transmission for a wide range of frequencies3.

Isotopic composition can dramatically affect thermal transport in nanotube and nanowire heat conduits. A record 50% increase in thermal conductivity for isotopically pure (11B) boron nitride nanotubes was recently measured, but the reason for this enhancement remains unclear. My collaborators and I examined thermal transport through boron nitride (BN) nanotubes using a NEGF formalism coupled with ab-initio force constants. We found an independent scatterer model for 10B defects can account for phonon isotope scattering found in natural boron nitride nanotubes4 and that, contrary to previous predictions, phonon localization will not be observable5 (Fig. 2).

In another work (PRB, 81, 045408 (2010)), we also examined how isotopic clusters could be used used to reduce thermal conductivity in graphene. One of the nice things about this approach is that isotopes have all the same electronic properties, so these clusters should have no effect on electrical conductivity in graphene.

Thermal Resistance at Interfaces

What happens to phonons when they encounter an interface between materials? This question is surprisingly difficult to answer and an accurate prediction of thermal resistance at interfaces is still not available. Many researchers still rely on acoustic mismatch models that lack atomistic detail and only consider the contribution of acoustic phonons to heat transfer. Molecular dynamic approaches have been used to address this problem. However, these approaches rely on empirical potentials that provide poor estimates for thermal transport. Nanoscale heat management, jet engine thermal barrier coatings, and thermoelectrics benefit from an accurate knowledge of thermal resistance at interfaces. I am working to expand the ab-initio NEGF phonon transport model to handle thermal transport across bulk interfaces. I am examining the thermal resistance caused by a thin silicon layer between two slabs of germanium (Ge-Si-Ge). In this work, I currently use the Siesta density functional package to relax the crystal structures and also determine the interatomic force constants between atoms using a real space approach. The Siesta code takes advantage of numerically truncated orbitals which lead to fast calculations for structures with a large amount of empty space. In all cases, fairly large cells must be considered in order to get a sufficient number of nearest neighbor interactions. The extracted force constants are then used to determine the phonon Green’s functions. I have used this approach successfully in the past to examine thermal transport in carbon nanotubes with defects and isotope scattering in carbon and boron-nitride nanotubes.

Structural Changes in Graphene during Oxidation

Graphene, a single honeycomb layer of carbon, could provide the ultimate limit in device miniaturization. However, critical questions remain on the practical design of devices and how chemical bonding affects graphene sheets. I am also combining my density functional expertise with EELS and STEM data from Prof. Andre Mkhoyan (Univ.
Minnesota
) and Prof. John Silcox’s group (Cornell) to decipher the atomic structure of graphene oxide. My structural relaxation calculations show clear evidence that oxygen distorts graphene, pulls neighboring carbon atoms above the plane, and transforms sp2 bonds to sp3 (Fig. 3). I have also been doing work determining the harmonic interatomic force constants for graphene and calculating the phonon dispersion.

Magnetic Nanostructures

Developing a new first principles code to model transport in magnetic nanostructures

Magnetic nanostructures offer unique advanced materials for future devices. The ability to create devices based both on the electron’s charge and spin has led to the current renaissance in magnetic storage media and a recent Nobel Prize. My interest in these systems began while studying magnetic multilayers with Bill Butler in the Materials Theory group at ORNL. Using Boltzmann transport techniques and a layered Korringa Kohn Rostoker approach, we examined how interface roughness and interdiffusion affect giant magnetoresistance6. During my post-doctoral fellowship at Sandia National Laboratories with Mark van Schilfgaarde, we developed a new electronic transport approach that incorporates a non-equilibrium Green’s function formalism within Linear Muffin Tin Orbital (LMTO) density functional approach7.

This new approach has proven to be an important tool in transport studies of magnetic nanostructures. I examined spin filtering in magnetically doped resonant tunneling devices and found that coupling spin split bands in electrical leads with quantum well states allows high tunneling magnetoresistance (TMR) ratios based on resonant tunneling8. For the past three years, I have also been collaborating with Evgeny Tsymbal’s group at the University of Nebraska to study tunneling magnetoresistance in systems such as Fe|MgO|Fe and Co|SrTiO3|Co. These studies have provided insight into the crucial role that interfaces play in magnetic transport. The first study9 indicated that the presence of a single layer of oxygen on a cobalt surface is enough to switch the spin polarization of conductance. In a recent Physical Review Letters10, we showed that the complex band structure of SrTiO3 provides efficient tunneling for only the minority electrons and that this system should have high TMR values. This approach is also capable of calculating current voltage characteristics for molecular junctions and metallic points contacts7.

Developing a new class of magnetic tunnel junctions based on reduced symmetry

Currently I collaborate with Prof. Buhrman and Prof. Muller at Cornell to understand how boron affects CoFeB|MgO|CoFeB tunnel junctions. The magnetic storage community has generally assumed that boron diffuses away from the oxide region during annealing. However, the Cornell groups have intriguing evidence that boron migrates into MgO during fabrication and improves TMR values, contrary to current device models.

To help shed light on this issue, I examined several different candidate magnesium pyroborate structures that may form in the oxide region. Based on EELS measurements and calculated energies from density functional calculations, it appears likely that Kotoite (Mg3B2O6) is forming in these junctions (Fig. 4).

The high tunnel magnetoresistance in current MgO based tunnel junctions is due to
symmetry selective filtering in MgO. In
particular, the FeCo majority carrier Delta1 band couples
efficiently with the Delta1 complex band in MgO, while minority carriers
can only couple through other complex bands that decay much faster. In order for Kotoite to be a strong candidate
for magnetic tunnel applications, there needs to be a clear separation in decay
rate of complex bands at the Fermi energy.

I recently calculated the complex band structure of this new junction
material and find a clear separation in terms of decay rate, indicating that a high TMR
value could be possible in these systems. What makes this new oxide particularly
interesting is that it has a lower symmetry crystal structure (orthorhombic)
than the two cubic ferromagnetic leads. This lower symmetry helps reduce tunneling
through the oxide for minority spin carriers and should enhance the TMR values By taking advantage of lower symmetry oxides,
it may be possible to develop a new class of magnetic tunnel junctions with
high TMR values.

Nanoscale Optoelectronics

Fig 5: Current-voltage characteristics for a (17,0) nanotube p-n junction under illumination, for a photon energy of 0.56 eV. Dashed line is for the dark junction. The optical power density is 860 W/cm2. The maximum power generated is Pmax = 49.33 pW as shown by the shaded area. (Stewart & Léonard, Nano Letters, 5, 219 (2005)).

While at Sandia National Laboratories, I also worked with Francois Léonard and developed a new non-equilibrium Green’s function tight binding code to model photocurrents in nanotube devices. This work resulted in a Physical Review Letters12 as well as a Nano Letters13. These studies provided the first estimate for power conversion efficiency in nanotube photodiodes. The power conversion efficiency was also found to increase as the nanotube diameter decreased. In addition, we found a unique scaling of the photocurrent with illuminated region that can be linked to density of state oscillations in the valence band induced by the p-n interface. Since current nanotube photodiodes are created by electrostatic gating, I am now examining how a central intrinsic region affects the photoresponse. In traditional semiconductors, the intrinsic region provides a larger region for photons to be absorbed in the device. However, in nanotube photodiodes, light is incident from above and the intrinsic region plays a more crucial role by changing the local charge distribution. I believe that the presence of an intrinsic region may be essential to achieve photocurrents.

Sandia National Labs has now made a version of the nanotube code available for distribution through the Office of Scientific and Technical Information (OSTI). Details can be found here.